A molecular simulation guided parametric modeling method of constitutive equations has attracted attention, which directly computes the physics-based structural parameters in molecular models without fitting stress-strain data. Using this method, we make a first attempt at constitutive relations of filled rubber by calculating amplification factors related to stress and strain distributions. The force field of the filled cis-1,4-polyisoprene (PI) rubber molecular model is obtained by the Boltzmann inversion method, which guarantees the accuracy of the structural parameters. The microstructural parameters and constitutive equations of the cross-linked, uncross-linked and the filled models are studied respectively. The calculated stress-strain curve of the cross-linked model is in the best agreement with the experimental one, while the curves of other models are in good agreement at small strain and have a certain degree of consistency at large strain.

一种分子模拟引导的本构方程参数化建模方法引起了人们的关注，该方法无需拟合应力-应变数据即可直接计算分子模型中基于物理的结构参数。使用这种方法，我们首次尝试通过计算与应力和应变分布相关的放大因子来研究填充橡胶的本构关系。填充顺式的力场-1,4-聚异戊二烯（PI）橡胶分子模型采用玻尔兹曼反演方法得到，保证了结构参数的准确性。分别研究了交联、未交联和填充模型的微观结构参数和本构方程。交联模型计算得到的应力-应变曲线与实验曲线吻合得最好，而其他模型的曲线在小应变下吻合较好，在大应变下具有一定的一致性。